Law enforcement officers responding to the scene shot the man multiple times in the lower body, according to police.
The suspect was transported to a nearby hospital, but his condition is not known.
One police officer suffered minor injuries during the incident at the club, which is near Miami.
The hotel's revenue during 2017 included more than $350,000 in campaign funds, the newspaper reported, the newspaper said.More news: Trump urged Merkel to abandon the "Nord stream-2"
Police wounded the man and took him into custody.
Perez said the man also draped an American flag over a counter in the hotel's lobby.
"We are not saying this is terrorism. we are not discounting anything at this point", according to Juan Perez, director of Miami-Dade Police.
Homeland Security and Secret Service are on the scene, and the Federal Bureau of Investigation is en route, Perez said.More news: Police respond to report of person with gun at Boulevard mall
Trump National Doral Golf Club, an 800-acre resort outside of Miami, is home to four championship golf courses, including the Blue Monster, which plays host to a PGA Tour event each year.
"These officers did not hesitate one second to engage this individual who was actively shooting in the lobby of the hotel", he said.
Fifteen of the 17 golf courses Trump owns worldwide-excluding his clubs in Dubai-made $221.9 million in 2017, according to his financial disclosure form for previous year that the U.S. Office of Government Ethics released on Wednesday. "They risked their lives knowing that they had to get in there to save lives in that hotel".More news: Careless Sundowns defending helps Barcelona triumph